Nuclear charge dependent interactions in the1pshell

A shell model analysis of the isobaric mass multiplets in the $1p$ shell shows that the isotensor charge dependent contribution (the coefficient of $T_z^2$ in the multiplet relationship) is, in all cases save one, underestimated when only electromagnetic interactions [including ${\left(\frac{v}{c}\right)}^2$ corrections, vacuum polarization, the effect of short range correlations, and finite neutron and proton size] are considered. Furthermore, the discrepancy is nearly twice as large for the seniority zero levels as for the higher seniority states, indicative of the omission of a short range charge dependent interaction. Since the free nucleon-nucleon scattering data indicate that the ($\mathrm{np}$) interaction is ∼2% more attractive than the ($\mathrm{nn}$), the effect of including such a charge dependent nuclear interaction on this coefficient is examined. When a Yukawa potential with range given by the $\pi$-meson Compton wavelength is taken for this potential it is found that theory and experiment can be brought into much better agreement.